CN110892659B - Apparatus and method for encoding a message having a target probability distribution of encoded symbols - Google Patents
Apparatus and method for encoding a message having a target probability distribution of encoded symbols Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/25—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM]
- H03M13/251—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM] with block coding
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0041—Arrangements at the transmitter end
- H04L1/0042—Encoding specially adapted to other signal generation operation, e.g. in order to reduce transmit distortions, jitter, or to improve signal shape
Abstract
The present application relates to a communication device for encoding a message to be transmitted over a communication channel. The communication device includes: a precoder to generate a precoded message based on the message and the polarity transformation; and a channel encoder for encoding the precoded message into a codeword based on the polarity transformation, wherein the codeword comprises a plurality of bits having a probability distribution; wherein the precoder is to generate the precoded message such that the channel encoder generates the plurality of bits of the codeword with the probability distribution matching a target probability distribution.
Description
Technical Field
The present application relates generally to encoding and decoding in a communication system. More particularly, the present application relates to an apparatus and method for encoding and decoding a message based on a polarity inversion.
Background
In order to achieve the capability of transmitting channels in a communication system, channel input symbols should have a certain probability distribution. For example, in the case of an Additive White Gaussian Noise (AWGN) channel, a Gaussian distribution is required to achieve the capability of the channel. However, in many practical communication systems, evenly distributed channel input symbols are used, resulting in a gap in capacity. This loss, also referred to as shaping loss, can be as high as 1.53dB over AWGN channels if uniformly distributed Quadrature Amplitude Modulation (QAM) symbols are used.
Shaping losses become significant especially in the case of high order modulation. One common method for transmission with higher order modulation is so-called bit-interleaved coded modulation (BICM), in which a message is first encoded into interleaved codewords by a channel encoder and then mapped to channel input symbols by a symbol mapper. In many communication systems, binary channel codes are used such that the codewords are binary vectors. In general, the distribution of 1's and 0's in the codeword is uniform, which also results in the channel input symbols also having a uniform distribution.
In the so-called non-uniform constellations (NUC) method, the possibility of using a symbol mapper with a non-uniform constellation is proposed. In this method, the output of the channel encoder is mapped to symbols that do not have a regular structure like QAM symbols, but have an optimized structure that helps to reduce the shaping loss. This method does not have any restrictions on the channel coding used, and this method is also referred to as geometry shaping. However, in this approach, due to the irregular constellation structure, the standard QAM symbol mapper and QAM demapper must be replaced by a more complex mapper/demapper.
The so-called Probabilistic Amplitude Shaping (PAS) method proposes to use a shaping encoder before using a channel encoder, which converts a uniformly distributed input message into a non-uniformly distributed sequence. The sequence is then encoded by a systematic channel encoder (i.e. the output of the channel encoder comprises the input of the encoder as a sub-vector) and then fed to a QAM symbol mapper. At the receiver, a QAM demapper may be used. After decoding the channel code, a shaping decoder processes the output of the channel code to recover the message.
Although this approach can eliminate almost all shaping loss, it still requires a shaping encoder and a shaping decoder, thus increasing the complexity and delay of the transmitter and receiver. This information is recovered after processing by both serial decoders, which may be suboptimal compared to a joint decoder. Furthermore, this method imposes a limitation on the channel coding used, which may be disadvantageous, since the channel encoder must be a systematic encoder.
Polarization code (see e.arikan, "Channel polarization: a method for constructing symmetric binary input memoryless Channel capability realization code (Channel polarization: a method for constraining the capacity-accessing codes for systematic combining-input memoryless channels)", IEEE trans. inf. the same, vol.55, No. 7, No. 3051-3073, p. 2009, 7) is a recently developed forward error correction scheme that can realize the capability of binary input discrete memoryless channels and can be used for Channel coding schemes. However, their performance under higher order modulation (e.g., BICM) is generally poor compared to other modern coding schemes. Furthermore, in general, the polarization codeword has P c (1) 0.5, i.e., the probability of having 1 and 0 in the codeword is equal.
In the prior art, there are some proposals (see mondell et al, "How to implement asymmetric channel capability (horizontal to horizontal the capacity of asymmetric channels)", Communication, Control, and Computing (Allerton), IEEE 52nd Annual meeting in 2014 (201452 nd annular Allerton reference on IEEE), 2014) to shape the output distribution of the polarized codewords so that P is the output distribution of P c (1) Not equal to 0.5. This is achieved by allowing some correlation between the transmitted information bits. In general, rather than transmitting k information bits, one transmits k-s information bits and generates s bits from the rest. These s bits are selected in such a way that the resulting codeword has a specific P c (1). These bits may also be referred to as shaping bits.
In the case of BICM, the BICM code may be combined with a polarization code (using a single polarization code in combination with high order modulation). This is compatible with many existing standards and is easy to implement. However, BICM with polar codes has poor performance compared to other alternatives.
In a multi-level coding (MLC) method, channel input symbols are considered as a combination of different bit levels. For each bit level, a different channel code is used. At the receiver, the demapping and decoding is done continuously, i.e. starting by demapping and decoding the first bit level. After the first bit level is processed, the output is used to demap and decode the second bit level, and until all bit levels are processed. This has shown that the performance of the polar code in combination with MLC is better than the conventional BICM. However, while good performance can be achieved, separate channel codes need to be designed for each bit level and several channel demapping and decoding processes need to be run, which can increase complexity and processing delay.
Accordingly, there is a need for improved communication devices and methods for encoding and decoding messages based on polarization codes to allow for a reduction in the gap in the capacity of the transmission channels.
Disclosure of Invention
It is an object of the present application to provide an improved communication device and method for encoding and decoding messages based on polarization codes, allowing to reduce the gap in the capacity of the transmission channel.
The foregoing and other objects are achieved by the subject matter of the independent claims. Further forms of realization are apparent from the dependent claims, the description and the accompanying drawings.
According to a first aspect, the application relates to a communication device for encoding a message to be transmitted over a communication channel, wherein the communication device comprises: a precoder to generate a precoded message based on the message and the polarity transformation; and a channel encoder for encoding the precoded message into a codeword based on the polarity transformation, wherein the codeword comprises a plurality of bits having a probability distribution; wherein the precoder is to generate the precoded message such that the channel encoder generates the plurality of bits of the codeword with the probability distribution matching a target probability distribution.
As used herein, polarity inversion may be based on corresponding to a matrix
Arika kernel or matrices with similar channel polarization effects.
Matching the probability distribution to the target probability distribution may include the precoder generating bits and/or symbols based on the target probability distribution. Further, this may include: the bits and/or symbols generated by the precoder (or a channel encoder processing the output of the precoder) have a probability distribution that is substantially equal to the target distribution, in particular the probability distribution has substantially the same mean and/or variance as the target distribution. For example, the distance between the probability distribution of the plurality of bits of the codeword and the target probability distribution may be given by a Kullback-Leibler distance.
Thus, the communication device according to the first aspect may generate a codeword with a non-uniform probability distribution of a plurality of bits. For example, the probability of a 1 occurring in a codeword may not be equal to 0.5. Thus, an improved communication device is provided, since the performance is significantly improved compared to conventional BICMs with polar codes, and compared to multi-level coding with polar codes.
In one possible implementation form of the communication device according to the first aspect, the precoder is a system precoder, i.e. the precoding message comprises the message.
This provides the advantage that at the receiver side for decoding the message to be transmitted, the inverse of the precoding operation is not required, resulting in a reduced complexity of the receiver.
In one possible implementation form of the communication device according to the first aspect, the communication device further comprises an interleaver for interleaving the plurality of bits of the codeword; and/or a modulator, in particular a symbol mapper, for mapping the codeword to one or more symbols for transmission over the communication channel.
Thus, an improved communication device is provided in which forward error correction is made more robust to burst errors due to, for example, the use of an interleaver.
In a possible implementation form of the communication device according to the first aspect, the polarity inversion is configured to take a frozen bit vector f as input, wherein the precoder is configured to generate the precoded message based on the message and the frozen bit vector f.
In a possible implementation form of the communication device according to the first aspect, the precoder is configured to generate the precoding message using one or more polar decoders, in particular a successive cancellation decoder (SC) or a successive cancellation list decoder (SCL).
Thus, an improved communication device is provided, since for example the use of an SC decoder provides the advantage of a communication device with lower complexity, whereas the use of an SCL decoder provides the advantage of a communication device with good performance.
In a possible implementation manner of the communication device according to the first aspect, the precoder is configured to take a vector v as an input, where the vector v includes an information bit vector e representing the message and the frozen bit vector f, and the precoder is configured to decompose the vector v into m subvectors v i 。
In one possible implementation form of the communication device according to the first aspect, the precoder comprises m sub-precoders, wherein each sub-precoder is configured to generate a respective sub-vector d representing a vector d of the precoding message i 。
In a possible implementation form of the communication device according to the first aspect, the precoder is configured to base the respective sub-vector d generated by the respective sub-precoder i And generating a vector d representing the precoded message.
In one possible implementation form of the communication device according to the first aspect, each sub-precoder comprises a polar decoder, in particular a successive cancellation decoder or a successive cancellation list decoder.
In a possible implementation form of the communication device according to the first aspect, each sub-vector v of the vector v is a vector v i Including a vector e i Sum vector f i Said vector e i Is a sub-vector of the information bit vector e, the vector f i Is the jellyA sub-vector of the bit vector f, and wherein each sub-precoder is configured to base a respective information bit sub-vector e i And the corresponding frozen bit subvectors f i Generating a corresponding sub-vector d representing said vector d of said pre-coded message i 。
In a possible implementation form of the communication device according to the first aspect, the target probability distribution comprises a plurality of target probabilities p i And wherein each sub-precoder is configured to base the respective target probability p i Generating a respective auxiliary channel decoder input vector y' i 。
This provides the advantage of generating codewords comprising different sub-vectors with different probabilities, so that after the symbol mapper an input symbol with the desired distribution can be obtained. Furthermore, this reduces the gap in the capacity of the transmission channel.
In a possible implementation form of the communication device according to the first aspect, each sub-precoder is further configured to base the respective information bit sub-vector e on the respective information bit sub-vector i And the corresponding frozen bit sub-vector f i Generating an auxiliary frozen bit sub-vector f i ′。
In a possible implementation form of the communication device according to the first aspect, each sub-precoder comprises a polar decoder, in particular a successive cancellation decoder or a successive cancellation list decoder, for decoding the respective auxiliary channel decoder input vector y' i And said corresponding auxiliary frozen bit subvectors f i ' generating a corresponding shaped bit vector s i Wherein each sub-precoder is configured to base on the corresponding information bit sub-vector e i And said corresponding shaped bit vector s i Generating the respective sub-vector d of the vector d representing the precoding information i 。
In one possible implementation of the communication device according to the first aspect, each sub-precoder is configured to shape the bit vector s by combining the corresponding shaping bit vector s i Corresponding to said information bit subvector e i Are connected to each otherIn the corresponding information bit sub-vector e i And said corresponding shaped bit vector s i Generating the respective sub-vector d representing the vector d of the pre-coded message i 。
According to a second aspect, the application relates to a method for encoding a message to be transmitted over a communication channel, wherein the method comprises: generating a pre-coded message based on the message and the polarity inversion; and encoding the precoded message into a codeword based on the polarity transformation, wherein the codeword comprises a plurality of bits having a probability distribution; wherein the pre-coded message is generated in a manner that generates a plurality of bits of the codeword with the probability distribution matching a target probability distribution.
According to a third aspect, the application relates to a computer program comprising program code for performing the method of the second aspect when executed on a computer or processor.
According to a fourth aspect, the application relates to a communication device for decoding a message received on a communication channel, wherein the communication device comprises: a channel decoder for decoding the message by polarity inversion from the frozen bit vector f, generating an estimate of a vector d comprising an information bit vector e and a shaped bit vector s.
In a possible implementation form of the communication device according to the fourth aspect, the channel decoder is configured to discard the shaped bit vector s.
In a possible implementation form of the communication device according to the fourth aspect, the channel decoder is configured to generate the sequence s 'based on an estimate of the vector d and to output an error message in case the sequence s' is not equal to the shaping bit vector s.
In a possible implementation form of the communication device according to the first aspect, the channel decoder comprises a list decoder for selecting a respective codeword from a list of codewords by selecting a codeword for which the sequence s' is equal to the shaping bit vector s.
The present application may be implemented in hardware and/or software.
Drawings
Other embodiments of the present application will be described with reference to the following drawings, in which:
fig. 1 shows a communication system comprising a communication device for encoding a message according to an embodiment and a communication device for decoding a message according to an embodiment;
FIG. 2 shows a schematic diagram of a channel encoder of a communication device for encoding a message according to an embodiment;
fig. 3 shows a schematic diagram of a communication device for decoding a message according to an embodiment;
FIG. 4 shows a schematic diagram of a polarity inversion used by a communication device for encoding a message according to an embodiment;
fig. 5 shows a schematic diagram of a communication device for encoding a message according to an embodiment;
FIG. 6 shows a schematic diagram of a polarity inversion used by a communication device for encoding messages according to an embodiment;
fig. 7 shows a schematic precoder diagram of a communication device for encoding a message according to an embodiment;
fig. 8 shows a schematic diagram of sub-precoders of a precoder for a communication device for encoding a message according to an embodiment; and
fig. 9 shows a schematic diagram of a method for encoding a message according to an embodiment.
The same reference numerals will be used for identical or at least functionally equivalent features in different drawings.
Detailed Description
The following description is made in conjunction with the accompanying drawings, which form a part of this disclosure, and which illustrate schematically specific aspects in which the present application may be implemented. It is to be understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present application. The following detailed description is, therefore, not to be taken in a limiting sense, as the scope of the present application is defined only by the appended claims.
For example, it is to be understood that the disclosure relating to the described method may also apply to a corresponding device or system configured to perform the method, and vice versa. For example, if a particular method step is described, the corresponding apparatus may comprise means for performing the described method step, even if the means is not explicitly described or shown in the figure. Furthermore, it should be understood that features of the various exemplary aspects described herein may be combined with each other, unless otherwise indicated.
Fig. 1 shows a schematic diagram of a communication system 100 according to one embodiment, the communication system 100 comprising a communication device 110 for encoding a message to be transmitted over a communication channel, and a communication device 120 for decoding the message.
The communication device 110 includes: a precoder 102 for generating a precoded message based on the message and the polarity transformation; and a channel encoder 104 for encoding the precoded message into a codeword based on the polarity inversion, wherein the codeword comprises a plurality of bits having a probability distribution; among other things, precoder 102 is used to generate a precoded message such that channel encoder 104 generates a plurality of bits of a codeword with a probability distribution that matches a target probability distribution, as will be described in more detail below.
As used herein, polarity inversion may be based on corresponding to a matrix
Arika kernel or matrices with similar channel polarization effects.
Matching the probability distribution to the target probability distribution may include precoder 102 generating bits and/or symbols based on the target probability distribution. Further, this may include: the bits and/or symbols generated by precoder 102 (or channel encoder 104 processing the output of the precoder) have a probability distribution substantially equal to the target distribution, in particular the probability distribution has substantially the same mean and/or variance as the target distribution. For example, the distance between the probability distribution of the plurality of bits of the codeword and the target probability distribution may be given by a Kullback-Leibler distance.
The communication device 110 can be readily configured to adapt the generation of the code words using other modifications of the polarization code, such as rate adaptation (puncturing, shortening and incremental redundancy methods) and other modifications of the polarization code, such as Parity Check (PC) polarization codes, Cyclic Redundancy Check (CRC) auxiliary/CA polarization codes, sub-polarization codes. Furthermore, the frozen bits of the polarity inversion may be randomly or pseudo-randomly selected, with randomness shared between the encoder and decoder.
The communication device 120 for decoding a message according to one embodiment comprises a channel decoder 120a for generating an estimate of a vector d comprising an information bit vector e and a shaping bit vector s from a frozen bit vector f by the communication device 110 for decoding a message based on a polarity inversion, as will be described in more detail below.
Fig. 2 shows a schematic diagram of a channel encoder 104 comprising a unit 104b for implementing a polarity inversion according to an embodiment.
In this embodiment, the channel encoder 104 is a polarity encoder according to an embodiment comprising a demultiplexer 104a and a polarity transform unit 104 b.
The demultiplexer 104a may be used to combine the vector d representing the precoded message with the frozen bit vector f to form a vector u of length N. In one embodiment, the obtained vector u has the following structure:
u i i e is I containing element d
u j J e is F containing element F
I∪F＝{0,1,...,N-1}
That is, vector u includes d bits (which includes information bit vector e representing the message and shaping bit vector s) at index I and includes frozen bits at index F that are known at the receiver side (i.e., communication device 120). The vector u may then be converted into a codeword c by using the polarity inversion implemented in unit 104b, which may be seen as the product of the vector u and the N × N polarization matrix.
Fig. 3 shows a schematic diagram of a communication device 120 for decoding a message according to an embodiment, the communication device 120 comprising a polar decoder 120a, in particular a Successive Cancellation (SC) decoder or a Successive Cancellation List (SCL) decoder 120 a.
In the embodiment shown in fig. 3, the SC or SCL polarity decoder 120a has four inputs: the channel output vector or received symbols y (also referred to as "channel decoder input vector"), such as log likelihood values (Inp1), a frozen bit vector F (Inp2), an index set of information bits I (Inp3), and an index set of frozen bits F (Inp 4). In addition, the SC or SCL polarity decoder 120a may have one output, namely a decoded information bit (Out1), namely a vector d representing the precoded message.
In embodiments of the present application, the channel encoder 104 shown in fig. 2 and/or the SC or SCL decoder 120b shown in fig. 3 may have additional parameters depending on the implementation, and some input parameters may be correlated such that some input parameters may be obtained from other input parameters. For example, if the set of information bits I is known, then the set of frozen bit indices F may also be obtained.
Fig. 4 shows a schematic diagram of a length-N polarity inversion implemented in unit 104b according to an embodiment.
The length-N polarity inversion implemented in unit 104b may be used to pass continuously executable log 2 (N) the polarization step generates a codeword of length N or a polarization codeword c. Thus, a polarization codeword c of length N can also be considered as a codeword obtained by using two polarization codes of length N/2, which can be further polarized in another step, as shown in fig. 4.
The communication device 110 may also include an interleaver 500 and/or a modulator, in particular a symbol mapper 502, for interleaving a plurality of bits of a codeword for mapping the codeword to one or more symbols for transmission over a communication channel.
Fig. 5 shows a schematic diagram of a communication device 110 for encoding a message according to one embodiment, the communication device 110 comprising a precoder 102, a channel encoder 104, an interleaver 500, and a symbol mapper 502.
In the embodiment shown in fig. 5, an information bit vector e representing a message is first processed by a precoder 102, which precoder 102 generates a vector d representing a precoded message. In this embodiment, the vector d representing the precoding message is (d ═ d 0 ,d 1 ,...,d n ) May be encoded by the channel encoder 104 to generate a code word, in particular a binary code word c. In one embodiment, P c (1) Not equal to 0.5, i.e. the binary codeword c may contain 1 s and 0 s with unequal probability distribution (note, P z (a) Representing the probability of the occurrence of element a in vector z).
As described above, in one embodiment, precoder 102 is configured to generate vector d in such a way that, after channel encoding by channel encoder 104, the resulting codeword c has certain characteristics in terms of probability distribution.
In embodiments of the present application, the features in terms of probability distribution may be described as follows: the codeword c comprises m subvectors (e.g. of equal length) c 1 ,...,c m And each of the m sub-vectors has a corresponding target probability, i.e.,
in an embodiment of the present application, the vector d includes the information bit vector e, i.e., the information bit vector e is a sub-vector of the vector d, i.e., the precoder 102 is a systematic precoder. This provides the following advantages: at the receiver or communication device 120, the inverse of the precoding operation is not required, allowing for a lower complexity receiver.
Furthermore, the binary codeword c may be shuffled or interleaved by an interleaver 500 to obtain a vector b. The vector b may then be fed to a symbol mapper 502.
Thus, in this embodiment, the output vector x of the symbol mapper 502 has a non-uniform probability distribution.
Fig. 6 shows a schematic diagram of an embodiment in which the precoder 102 includes first and second sub-precoders.
In an embodiment of the application, m different parts of the length N vector u are generated in such a way that each of the m parts has some correlation or different probability distribution in its bits. In particular, m may correspond to the bit level of the higher order modulation.
In particular, in fig. 6, an example is shown where m-2, where a length N vector u is composed of two sub-vectors u of length N/2 1 And u 2 And (4) forming. The sub-vector u may be generated by using the first and second sub-precoders 1 And u 2 . This may mean u i The included bits have some correlation. If by a single polarity inversion pair u implemented in the length-N unit 104b 1 u 2 ]The encoding is performed, then the resulting codeword c may have the desired properties described above.
Subvector u 1 And u 2 Information bits and freeze bits may be included. Furthermore, in the embodiments of the present application, the sub-vector u 1 And u 2 Shaping bits may also be included that are based on the information bits and the frozen bits and that facilitate convergence of the output distribution to a target probability distribution.
The exemplary process explained in the context of fig. 6 can also be extended to larger values of m. For example, by dividing the vector u into m-4 and using two additional polarization steps, a single polarization codeword c with four different bit distributions can be obtained.
Fig. 7 shows a schematic diagram of precoder 102 of a communication device 110 according to an embodiment.
In the embodiment shown in fig. 7, precoder 102 comprises two multiplexing units 102a-1, 102a-2, m sub-precoders 102b-1, …, 102b-m, and a demultiplexing unit 104 a.
The precoder 102 may be used to decompose a vector v, comprising an information bit vector e and a frozen bit vector f, into m subvectors v i Where each subvector is upsilon i Including a vector e i Sum vector f i The vector e i Is a sub-vector of an information bit vector e, the vector f i Are sub-vectors of the frozen bit vector f.
In one embodiment, multiplexing unit 102a-1 is used to decompose information bit vector e into m vectors e i And the multiplexing unit 102a-1 is arranged to decompose the frozen bit vector f into m vectors f i 。
In one embodiment, each of the m sub-precoders 102b-1, …, 102b-m is configured to be based on a respective vector e i Vector f i And corresponding target probability p i Generating a corresponding sub-vector d representing a vector d of pre-coded messages i Each sub-vector of (a).
In one embodiment, demultiplexing unit 104a is configured to demultiplex by combining m subvectors d i A vector d representing the precoded message is generated.
In one embodiment, precoder 102 comprises an SC or SCL polarity decoder 120a as already described in the context of fig. 3.
Fig. 8 shows a schematic diagram of a detailed view of one of the m sub-precoders 102b-1, …, 102b-m shown in fig. 7.
In the embodiment shown in fig. 8, the sub-precoder 102b-1 comprises a unit 800, which unit 800 is configured to base the respective target probability p i Generating a respective auxiliary channel decoder input vector y' i . In one embodiment, the channel decoder input vector is a length-N vector (the same length as the codeword length) in which the elements have the same value log (p) i /(1-p i ))。
Furthermore, in this embodiment, the corresponding information bit subvectors e i And a corresponding frozen bit sub-vector f i Are combined in demultiplexer 802 to generate vector f i '. Form a vector f i Bits of' can be used asThe auxiliary freeze bits of the SC/SCL decoder 804 in the sub-precoder 102b (Inp 2). Further, the SC/SCL decoder 804 in the sub-precoder 102b-1 may use the corresponding secondary channel decoder input vector y' i As a channel output vector (Inp 1). The output of the SC/SCL polarity decoder 804 may include a corresponding shaped bit vector s i (Out1)。
Furthermore, the demultiplexing unit 806 may be adapted to shape the corresponding bit vector s i Connected to corresponding information bit sub-vectors e i To generate a corresponding vector d i 。
The sub-precoder 102b-1 provides the advantage that the vector d comprises e as a sub-vector, which provides the advantage of easy decoding at the receiving communication device 120 side.
Furthermore, the sub-precoder 102b-1 provides the advantage of using the SC or SCL decoder 804 to generate a codeword c, which is already part of the polar transmission chain, i.e., the decoder 120a of the receiving communication device 120 shown in fig. 3. In other words, precoder 102 may be implemented using existing hardware on a chip that includes communication device 110 and communication device 120.
Fig. 9 illustrates a schematic diagram of a method 900 for encoding a message to be transmitted over a communication channel in accordance with one embodiment.
The method 900 includes the following steps: generating 902 a precoded message based on the message and the polarity transformation, and encoding 904 the precoded message into a codeword based on the polarity transformation, wherein the codeword comprises a plurality of bits having a probability distribution, wherein the precoded message is generated in a manner that generates the plurality of bits of the codeword with the probability distribution matching a target probability distribution.
While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations or embodiments, such feature or aspect may be combined with one or more other features or aspects of the other implementations or embodiments and may be desired and advantageous for any given or particular application. Furthermore, for words used in the detailed description or claims: "including," having, "or other variations thereof, are intended to be inclusive in a manner similar to the term" comprising. Also, the words "exemplary," "e.g.," and "such as" are used merely as examples and are not optimal or optimal. The terms "coupled" and "connected," along with their derivatives, may be used. It will be understood that these terms may be used to indicate that two elements co-operate or interact with each other, whether or not they are in direct physical or electrical contact, or they are not in direct contact with each other.
Although specific aspects have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein.
Although the elements in the claims are recited in a particular sequence of corresponding labeling, unless the claims otherwise imply a particular sequence for implementing some or all of the elements, these elements are not necessarily intended to be limited to being implemented in that particular sequence.
Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, one skilled in the art will readily recognize that there are many applications for this application other than those described herein. While the present application has been described with reference to one or more particular embodiments, those skilled in the art will recognize that many changes may be made thereto without departing from the scope of the present application. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application may be practiced otherwise than as specifically described herein.
Claims (10)
1. A communication device for encoding a message to be transmitted over a communication channel, the communication device comprising:
a precoder to generate a precoded message based on the message and the polarity transformation; and a channel encoder for encoding the precoded message into a codeword based on the polarity transformation, wherein the codeword comprises a plurality of bits having a probability distribution; wherein the precoder is to generate the precoded message such that the channel encoder generates the plurality of bits of the codeword with the probability distribution matching a target probability distribution;
the precoder is a system precoder, i.e. the precoding message comprises the message;
the polarity inversion is to take as input a frozen bit vector f, and wherein the precoder is to generate the precoded message based on the message and the frozen bit vector f;
the precoder is configured to generate the precoding message using one or more polar decoders, in particular a successive cancellation decoder or a successive cancellation list decoder; alternatively, the first and second electrodes may be,
the precoder is configured to take as input a vector v comprising an information bit vector e representing the message and the frozen bit vector f, and wherein the precoder is configured to decompose the vector v into m subvectors v i 。
2. Communication device according to claim 1, characterized in that the communication device further comprises an interleaver and/or a modulator, in particular a symbol mapper, for interleaving the plurality of bits of the codeword for transmission on the communication channel.
3. The communications device of claim 1, wherein the precoder comprises m sub-precoders, wherein each sub-precoder is configured to generate a respective sub-vector d representing a vector d of the precoded message i 。
4. The communications device of claim 3, wherein said precoder is configured to base said respective sub-vectors d generated by said respective sub-precoders on i Generating a presentationA vector d of the precoded message.
5. The communication device according to claim 3 or 4, wherein each sub-precoder comprises a polar decoder, in particular a successive cancellation decoder or a successive cancellation list decoder.
6. A communication device according to claim 3 or 4, wherein each subvector of said vectors v is vector v i Including a vector e i Sum vector f i The vector e i Is a sub-vector of the information bit vector e, the vector f i Is a sub-vector of the frozen bit vector f, and wherein each sub-precoder is configured to base a respective information bit sub-vector e i And a corresponding frozen bit sub-vector f i Generating a corresponding sub-vector d representing said vector d of said pre-coded message i 。
7. The communication device of claim 6, wherein the target probability distribution comprises a plurality of target probabilities p i And wherein each of the sub-precoders is configured to be based on the corresponding target probability p i Generating a respective auxiliary channel decoder input vector y' i 。
8. The communications device of claim 7, wherein each sub-precoder is further configured to base the corresponding information bit sub-vector e i And the corresponding frozen bit sub-vector f i Generating an auxiliary frozen bit sub-vector f i ′。
9. Communication device according to claim 8, wherein each sub-precoder comprises a polar decoder, in particular a successive cancellation decoder or a successive cancellation list decoder, for inputting a vector y 'based on the corresponding auxiliary channel decoder' i And said corresponding auxiliary frozen bit sub-vector f i ' generating a corresponding shaped bit vector s i And wherein each of said sub-precoders is configured to base on said corresponding information bit sub-vector e i And said corresponding shaped bit vector s i Generating the respective sub-vector d of the vector d representing the precoding information i 。
10. The communication device of claim 9, wherein each sub-precoder is configured to shape the bit vector s by dividing the corresponding shaped bit vector s i The information bit sub-vector e corresponding to the i Connected based on the corresponding information bit subvectors e i And said corresponding shaped bit vector s i Generating the respective sub-vector d representing the vector d of the pre-coded message i 。
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